Exact Confidence Intervals for Proportions Estimated by Group Testing

In plant disease assessment, estimation of the proportion of infected units in a population can be greatly facilitated by group testing. Further gains may be possible by the sequential testing of groups of different sizes. The construction of exact confidence intervals is considered here for problems involving unequal sized groups. The recommended method uses an ordering of outcomes based on their associated maximum likelihood estimates. The method is compared with the technique proposed by Sterne (1954, Biometrika 41, 275-278) in which outcomes are ordered according to their probability. An assessment of the prevalence of viruses in carnation populations is used to illustrate the method. made by such pooling or group testing. A series of tests in which all groups test positive is of very limited value, but the presence of at least one negative group often provides enough information to make the pooling of units worthwhile. This study arose from an assessment of carnation populations in nursery glasshouses in Victoria, Australia. The purpose of the investigation was to estimate the prevalence of several viruses in carnations grown by a range of growers. Following the collection of a sample of leaves from a glasshouse (a leaf being assumed to accurately indicate a plant's infection status), it was possible to reliably test large groups of leaves for the presence of a virus using enzyme-linked immunosorbent assay (ELISA). The cost of sampling a leaf was small compared to that of performing an ELISA, and so group testing was seen as a likely way of improving precision within the available resources. Group testing first appeared in the statistics literature in the context of identifying individual infected units in a population. Dorfman (1943) proposed the pooling of blood samples in testing for the syphilis antigen, followed by the retesting of individuals in any group found to be infected. This has spawned a considerable body of literature on group testing procedures for efficient identification. The other major area which has emerged is that in which estimation of the prevalence of a disease is much more important than the identification of infected units. This was the case in the assessment of the Victorian carnation industry, and it is estimation with which this paper is concerned. Most of the work in this area has been applied to the problem of estimating the proportion of vectors transmitting a plant or animal virus (Gibbs and Gower, 1960; Thompson, 1962; Walter, Hildreth, and Beaty, 1980; Romanow, Moyer, and Kennedy, 1986; Swallow, 1987). In those studies the vectors